Limit oscillatory cycles in the single mode flutter of a plate

The development of the single mode flutter of an elastic plate in a supersonic gas flow is investigated in a non-linear formulation. In the case of a small depression in the instability zone, there is a unique limit cycle corresponding to a unique growing mode. Several new non-resonant limit cycles arise when a second increasing mode appears and the domains of their existence and stability are found. Limit cycles with an internal resonance, in which there is energy exchange between the modes, can exist for the same parameters. Relations between the amplitudes of the limit cycles and the parameters of the problem are obtained that enable one to estimate the risk of the onset of flutter.